%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG368-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:48:23 AM UTC 2026
% Result : Unsatisfiable 226.31s 59.32s
% Output : CNFRefutation 226.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 23
% Syntax : Number of clauses : 77 ( 37 unt; 14 nHn; 57 RR)
% Number of literals : 149 ( 42 equ; 70 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 73 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_abs__add__one__gt__zero_0,axiom,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uHOL$uOabs$u$uclass$uOabs'(X0,'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ).
cnf(cls_exp__not__eq__zero_0,axiom,
( 'c$uTranscendental$uOexp'(X1,X0) != 'c$uHOL$uOzero$u$uclass$uOzero'(X0)
| ~ 'class$uRealVector$uOreal$u$unormed$u$ufield'(X0)
| ~ 'class$uSEQ$uObanach'(X0) ) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ 'c$uHOL$uOord$u$uclass$uOless'(X2,X1,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOpreorder'(X0) ) ).
cnf(cls_exp__ln_0,axiom,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'c$uTranscendental$uOexp'('c$uTranscendental$uOln'(X0),'tc$uRealDef$uOreal') = X0 ) ).
cnf(cls_real__less__def_0,axiom,
( ~ 'c$uHOL$uOord$u$uclass$uOless'(X0,X1,'tc$uRealDef$uOreal')
| 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal') ) ).
cnf(cls_dist__commute_0,axiom,
( 'c$uRealVector$uOdist$u$uclass$uOdist'(X1,X2,X0) = 'c$uRealVector$uOdist$u$uclass$uOdist'(X2,X1,X0)
| ~ 'class$uRealVector$uOmetric$u$uspace'(X0) ) ).
cnf(cls_dist__complex__def_0,axiom,
'c$uRealVector$uOdist$u$uclass$uOdist'(X0,X1,'tc$uComplex$uOcomplex') = 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOminus$u$uclass$uOminus'(X0,X1,'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') ).
cnf(cls_norm__zero_0,axiom,
( 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOzero$u$uclass$uOzero'(X0),X0) = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ) ).
cnf(cls_poly__0_0,axiom,
( 'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0)),X1,X0) = 'c$uHOL$uOzero$u$uclass$uOzero'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOcomm$u$usemiring$u$u0'(X0) ) ).
cnf(cls_ep_0,axiom,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ue','tc$uRealDef$uOreal') ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( 'c$uHOL$uOord$u$uclass$uOless'(X1,X2,X0)
| 'c$uHOL$uOord$u$uclass$uOless'(X2,X1,X0)
| X1 = X2
| ~ 'class$uOrderings$uOlinorder'(X0) ) ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( 'c$uHOL$uOminus$u$uclass$uOminus'(X1,X1,X0) = 'c$uHOL$uOzero$u$uclass$uOzero'(X0)
| ~ 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0) ) ).
cnf(cls_diff__0__right_0,axiom,
( 'c$uHOL$uOminus$u$uclass$uOminus'(X1,'c$uHOL$uOzero$u$uclass$uOzero'(X0),X0) = X1
| ~ 'class$uOrderedGroup$uOgroup$u$uadd'(X0) ) ).
cnf(cls_conjecture_2,negated_conjecture,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOminus$u$uclass$uOminus'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'('v$uz','v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'v$ue','tc$uRealDef$uOreal') ) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
'class$uRealVector$uOreal$u$unormed$u$ufield'('tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__SEQ_Obanach,axiom,
'class$uSEQ$uObanach'('tc$uRealDef$uOreal') ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
'class$uRing$u$uand$u$uField$uOcomm$u$usemiring$u$u0'('tc$uComplex$uOcomplex') ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex') ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom,
'class$uOrderedGroup$uOab$u$ugroup$u$uadd'('tc$uComplex$uOcomplex') ).
cnf(clsarity_Complex__Ocomplex__RealVector_Ometric__space,axiom,
'class$uRealVector$uOmetric$u$uspace'('tc$uComplex$uOcomplex') ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
'class$uOrderedGroup$uOgroup$u$uadd'('tc$uComplex$uOcomplex') ).
cnf(c116,plain,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uHOL$uOabs$u$uclass$uOabs'(X0,'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_abs__add__one__gt__zero_0]) ).
cnf(c496,plain,
( 'c$uTranscendental$uOexp'(X1,X0) != 'c$uHOL$uOzero$u$uclass$uOzero'(X0)
| ~ 'class$uRealVector$uOreal$u$unormed$u$ufield'(X0)
| ~ 'class$uSEQ$uObanach'(X0) ),
inference(clausification,[status(esa)],[cls_exp__not__eq__zero_0]) ).
cnf(c560,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'(X2,X1,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOpreorder'(X0) ),
inference(clausification,[status(esa)],[cls_less__le__not__le_1]) ).
cnf(c586,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'c$uTranscendental$uOexp'('c$uTranscendental$uOln'(X0),'tc$uRealDef$uOreal') = X0 ),
inference(clausification,[status(esa)],[cls_exp__ln_0]) ).
cnf(c592,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'(X0,X1,'tc$uRealDef$uOreal')
| 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal') ),
inference(clausification,[status(esa)],[cls_real__less__def_0]) ).
cnf(c719,plain,
( 'c$uRealVector$uOdist$u$uclass$uOdist'(X1,X2,X0) = 'c$uRealVector$uOdist$u$uclass$uOdist'(X2,X1,X0)
| ~ 'class$uRealVector$uOmetric$u$uspace'(X0) ),
inference(clausification,[status(esa)],[cls_dist__commute_0]) ).
cnf(c806,plain,
'c$uRealVector$uOdist$u$uclass$uOdist'(X0,X1,'tc$uComplex$uOcomplex') = 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOminus$u$uclass$uOminus'(X0,X1,'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[cls_dist__complex__def_0]) ).
cnf(c820,plain,
( 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOzero$u$uclass$uOzero'(X0),X0) = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ),
inference(clausification,[status(esa)],[cls_norm__zero_0]) ).
cnf(c821,plain,
( 'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0)),X1,X0) = 'c$uHOL$uOzero$u$uclass$uOzero'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOcomm$u$usemiring$u$u0'(X0) ),
inference(clausification,[status(esa)],[cls_poly__0_0]) ).
cnf(c823,plain,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ue','tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_ep_0]) ).
cnf(c828,plain,
( 'c$uHOL$uOord$u$uclass$uOless'(X1,X2,X0)
| 'c$uHOL$uOord$u$uclass$uOless'(X2,X1,X0)
| X1 = X2
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(clausification,[status(esa)],[cls_not__less__iff__gr__or__eq_0]) ).
cnf(c833,plain,
( 'c$uHOL$uOminus$u$uclass$uOminus'(X1,X1,X0) = 'c$uHOL$uOzero$u$uclass$uOzero'(X0)
| ~ 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_eq__iff__diff__eq__0_0]) ).
cnf(c835,plain,
( 'c$uHOL$uOminus$u$uclass$uOminus'(X1,'c$uHOL$uOzero$u$uclass$uOzero'(X0),X0) = X1
| ~ 'class$uOrderedGroup$uOgroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_diff__0__right_0]) ).
cnf(c851,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOminus$u$uclass$uOminus'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'('v$uz','v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'v$ue','tc$uRealDef$uOreal') ),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c926,plain,
'class$uRealVector$uOreal$u$unormed$u$ufield'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__RealVector_Oreal__normed__field]) ).
cnf(c950,plain,
'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(c951,plain,
'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(c955,plain,
'class$uSEQ$uObanach'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__SEQ_Obanach]) ).
cnf(c966,plain,
'class$uRing$u$uand$u$uField$uOcomm$u$usemiring$u$u0'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0]) ).
cnf(c969,plain,
'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c977,plain,
'class$uOrderedGroup$uOab$u$ugroup$u$uadd'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add]) ).
cnf(c983,plain,
'class$uRealVector$uOmetric$u$uspace'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[clsarity_Complex__Ocomplex__RealVector_Ometric__space]) ).
cnf(c986,plain,
'class$uOrderedGroup$uOgroup$u$uadd'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add]) ).
cnf(d0,plain,
'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c820,c969]) ).
cnf(d1,plain,
'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),X0,'tc$uComplex$uOcomplex') = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),
inference(resolution,[status(thm)],[c821,c966]) ).
cnf(d2,plain,
'c$uRealVector$uOdist$u$uclass$uOdist'(X0,X1,'tc$uComplex$uOcomplex') = 'c$uRealVector$uOdist$u$uclass$uOdist'(X1,X0,'tc$uComplex$uOcomplex'),
inference(resolution,[status(thm)],[c719,c983]) ).
cnf(d3,plain,
'c$uHOL$uOminus$u$uclass$uOminus'(X0,'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') = X0,
inference(resolution,[status(thm)],[c835,c986]) ).
cnf(d4,plain,
'c$uRealVector$uOdist$u$uclass$uOdist'(X0,'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') = 'c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,'tc$uComplex$uOcomplex'),
inference(superposition,[status(thm)],[d3,c806]) ).
cnf(d5,plain,
'c$uRealVector$uOdist$u$uclass$uOdist'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),X0,'tc$uComplex$uOcomplex') = 'c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,'tc$uComplex$uOcomplex'),
inference(superposition,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
'c$uHOL$uOminus$u$uclass$uOminus'(X0,X0,'tc$uComplex$uOcomplex') = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),
inference(resolution,[status(thm)],[c833,c977]) ).
cnf(d7,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOdist$u$uclass$uOdist'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'('v$uz','v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'v$ue','tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal') ),
inference(demodulation,[status(thm)],[c851,c806]) ).
cnf(d8,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOdist$u$uclass$uOdist'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'v$ue','tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal') ),
inference(demodulation,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal')
| 'c$uHOL$uOord$u$uclass$uOless'('v$ue','c$uRealVector$uOdist$u$uclass$uOdist'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal')
| 'v$ue' = 'c$uRealVector$uOdist$u$uclass$uOdist'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[d8,c828]) ).
cnf(d10,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal')
| 'c$uHOL$uOord$u$uclass$uOless'('v$ue','c$uRealVector$uOdist$u$uclass$uOdist'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'v$ue' = 'c$uRealVector$uOdist$u$uclass$uOdist'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') ),
inference(demodulation,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal')
| 'c$uHOL$uOord$u$uclass$uOless'('v$ue','c$uRealVector$uOdist$u$uclass$uOdist'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'v$ue' = 'c$uRealVector$uOdist$u$uclass$uOdist'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') ),
inference(demodulation,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal')
| 'c$uHOL$uOord$u$uclass$uOless'('v$ue','c$uRealVector$uOdist$u$uclass$uOdist'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'v$ue' = 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') ),
inference(demodulation,[status(thm)],[d11,d5]) ).
cnf(d13,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal')
| 'c$uHOL$uOord$u$uclass$uOless'('v$ue','c$uRealVector$uOdist$u$uclass$uOdist'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'v$ue' = 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') ),
inference(demodulation,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal')
| 'c$uHOL$uOord$u$uclass$uOless'('v$ue','c$uRealVector$uOdist$u$uclass$uOdist'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'v$ue' = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ),
inference(demodulation,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal')
| 'c$uHOL$uOord$u$uclass$uOless'('v$ue','c$uRealVector$uOdist$u$uclass$uOdist'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'v$ue' = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ),
inference(demodulation,[status(thm)],[d14,d2]) ).
cnf(d16,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal')
| 'c$uHOL$uOord$u$uclass$uOless'('v$ue','c$uRealVector$uOdist$u$uclass$uOdist'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'v$ue' = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ),
inference(demodulation,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal')
| 'c$uHOL$uOord$u$uclass$uOless'('v$ue','c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'c$uHOL$uOminus$u$uclass$uOminus'(hAPP('v$ux',X0),'v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'v$ue' = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ),
inference(demodulation,[status(thm)],[d16,d5]) ).
cnf(d18,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal')
| 'c$uHOL$uOord$u$uclass$uOless'('v$ue','c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'v$ue' = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ),
inference(demodulation,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal')
| 'c$uHOL$uOord$u$uclass$uOless'('v$ue','c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'v$ue' = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ),
inference(demodulation,[status(thm)],[d18,d0]) ).
cnf(d20,plain,
( 'c$uHOL$uOord$u$uclass$uOless'('v$ue','c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'v$ue' = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c951,d19]) ).
cnf(d21,plain,
'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ue','tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c592,c823]) ).
cnf(d22,plain,
( ~ 'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('v$ue','c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c560,d21]) ).
cnf(d23,plain,
~ 'c$uHOL$uOord$u$uclass$uOless'('v$ue','c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c950,d22]) ).
cnf(d24,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'v$ue' = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[d23,d20]) ).
cnf(d25,plain,
'c$uTranscendental$uOexp'('c$uTranscendental$uOln'('v$ue'),'tc$uRealDef$uOreal') = 'v$ue',
inference(resolution,[status(thm)],[c586,c823]) ).
cnf(d26,plain,
( ~ 'class$uSEQ$uObanach'('tc$uRealDef$uOreal')
| ~ 'class$uRealVector$uOreal$u$unormed$u$ufield'('tc$uRealDef$uOreal')
| 'v$ue' != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ),
inference(superposition,[status(thm)],[d25,c496]) ).
cnf(d27,plain,
( ~ 'class$uSEQ$uObanach'('tc$uRealDef$uOreal')
| 'v$ue' != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c926,d26]) ).
cnf(d28,plain,
'v$ue' != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c955,d27]) ).
cnf(d29,plain,
~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[d28,d24]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[d29,c116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG368-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.53 % Computer : n004.cluster.edu
% 0.09/0.53 % Model : x86_64 x86_64
% 0.09/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.53 % Memory : 8046.5625MB
% 0.09/0.53 % OS : Linux 6.8.0-71-generic
% 0.09/0.53 % CPULimit : 300
% 0.09/0.53 % WCLimit : 300
% 0.09/0.53 % DateTime : Sat Sep 26 21:55:23 UTC 2026
% 0.09/0.53 % CPUTime :
% 0.09/0.53 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 226.31/59.32 % SZS status Unsatisfiable for theBenchmark.p
% 226.31/59.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------